The document summarizes analyses of two heart disease datasets: LA Heart and Cardiovas. For LA Heart, logistic regression found systolic blood pressure highly predicts heart disease probability, while other factors were less predictive. For Cardiovas, multiple regressions found hemoglobin A1C levels best explained by waist size, age, cholesterol, and blood glucose. Blood glucose was best explained by age, and other factors showed moderate-high significance. Overall, the analyses indicate systolic blood pressure and hemoglobin A1C/blood glucose levels along with associated risk factors provide useful information for understanding heart disease outcomes.
The learning speed of the feed forward neural
network takes a lot of time to be trained which is a major
drawback in their applications since the past decades. The
key reasons behind may be due to the slow gradient-based
learning algorithms which are extensively used to train the
neural networks or due to the parameters in the networks
which are tuned iteratively using some learning algorithms.
Thus, in order to eradicate the above pitfalls, a new learning
algorithm was proposed known as Extreme Learning Machines
(ELM). This algorithm tries to compute Hidden-layer-output
matrix that is made of randomly assigned input layer and
hidden layer weights and randomly assigned biases. Unlike the
other feedforward networks, ELM has the access of the whole
training dataset before going into the computation part. Here,
we have devised a new two-layer-feedforward network (TFFN)
for ELM in a new manner with randomly assigning the weights
and biases in both the hidden layers, which then calculates the
output-hidden layer weights using the Moore-Penrose generalized
inverse. TFFN doesn’t restricts the algorithm to fix the number
of hidden neurons that the algorithm should have. Rather it
searches the space which gives an optimized result in the neurons
combination in both the hidden layers. This algorithm provides a
good generalization capability than the parent Extreme Learning
Machines at an extremely fast learning speed. Here, we have
experimented the algorithm on various types of datasets and
various popular algorithm to find the performances and report
a comparison.
Fat, cholesterol, calcium, and other substances found in the blood can build up over time in the arteries. Over time, a sticky substance called plaque can form, hardening and narrowing these vessels, and limiting the flow of oxygen-rich blood through the body. Of all the atherosclerotic plaque constituents, cholesterol has been strongly linked to heart disease. Current expert opinion holds that people with high LDL-cholesterol levels may have atherosclerotic plaques that are more likely to burst, resulting in blood clots and downstream events such as strokes and heart disease.
This slide deck provides basic information about cholesterol and information obtained from a variety of sources.
The learning speed of the feed forward neural
network takes a lot of time to be trained which is a major
drawback in their applications since the past decades. The
key reasons behind may be due to the slow gradient-based
learning algorithms which are extensively used to train the
neural networks or due to the parameters in the networks
which are tuned iteratively using some learning algorithms.
Thus, in order to eradicate the above pitfalls, a new learning
algorithm was proposed known as Extreme Learning Machines
(ELM). This algorithm tries to compute Hidden-layer-output
matrix that is made of randomly assigned input layer and
hidden layer weights and randomly assigned biases. Unlike the
other feedforward networks, ELM has the access of the whole
training dataset before going into the computation part. Here,
we have devised a new two-layer-feedforward network (TFFN)
for ELM in a new manner with randomly assigning the weights
and biases in both the hidden layers, which then calculates the
output-hidden layer weights using the Moore-Penrose generalized
inverse. TFFN doesn’t restricts the algorithm to fix the number
of hidden neurons that the algorithm should have. Rather it
searches the space which gives an optimized result in the neurons
combination in both the hidden layers. This algorithm provides a
good generalization capability than the parent Extreme Learning
Machines at an extremely fast learning speed. Here, we have
experimented the algorithm on various types of datasets and
various popular algorithm to find the performances and report
a comparison.
Fat, cholesterol, calcium, and other substances found in the blood can build up over time in the arteries. Over time, a sticky substance called plaque can form, hardening and narrowing these vessels, and limiting the flow of oxygen-rich blood through the body. Of all the atherosclerotic plaque constituents, cholesterol has been strongly linked to heart disease. Current expert opinion holds that people with high LDL-cholesterol levels may have atherosclerotic plaques that are more likely to burst, resulting in blood clots and downstream events such as strokes and heart disease.
This slide deck provides basic information about cholesterol and information obtained from a variety of sources.
White paper looking at the hypothesis that dietary fat leads to high cholesterol, which leads to cardiovascular disease and mortality. But does the research really show that saturated fat is really bad for you?
Coronary Artery Disease and Menopause: A Consequence of Adverse Lipid Changesiosrjce
IOSR Journal of Dental and Medical Sciences is one of the speciality Journal in Dental Science and Medical Science published by International Organization of Scientific Research (IOSR). The Journal publishes papers of the highest scientific merit and widest possible scope work in all areas related to medical and dental science. The Journal welcome review articles, leading medical and clinical research articles, technical notes, case reports and others.
Electrolyte abnormalities in cardiovascular emergencies are widely studied worldwide as they are mostly found to be associated with cardiovascular morbidity and mortality. The objective of this study was to compare the serum sodium. potassium,calcium and magnesium concentrations of normal healthy individuals with first time diagnosed patients of valvular heart disease and myocardial infarction as well as to evaluate the prognostic value in the severity and outcome of valvular heart disease and myocardial infarction.Following biochemical tests, the mean serum sodium concentrations in both valvular heart disease and myocardial infarction patients were signifi cantly (p ˂ 0.05) higher than normal healthy persons. The mean potassium and calcium concentrations in valvular heart disease and myocardial patients were signifi cantly (p ˂ 0.05) high and low respectively when compared with normal healthy individuals. In comparison to normal healthy persons, respective groups of valvular heart disease and myocardial infarction patients showed a non-signifi cant (p = 0.6123) and a signifi cant (p ˂ 0.05) reduction in mean serum magnesium concentrations. Moreover, comparative analysis of mean serum electrolytes among valvular heart disease and myocardial infarction patients showed a signifi cant low sodium, high potassium, calcium and magnesium concentrations in contrast to signifi cant high sodium, low potassium, calcium and magnesium concentrations respectively.
White paper looking at the hypothesis that dietary fat leads to high cholesterol, which leads to cardiovascular disease and mortality. But does the research really show that saturated fat is really bad for you?
Coronary Artery Disease and Menopause: A Consequence of Adverse Lipid Changesiosrjce
IOSR Journal of Dental and Medical Sciences is one of the speciality Journal in Dental Science and Medical Science published by International Organization of Scientific Research (IOSR). The Journal publishes papers of the highest scientific merit and widest possible scope work in all areas related to medical and dental science. The Journal welcome review articles, leading medical and clinical research articles, technical notes, case reports and others.
Electrolyte abnormalities in cardiovascular emergencies are widely studied worldwide as they are mostly found to be associated with cardiovascular morbidity and mortality. The objective of this study was to compare the serum sodium. potassium,calcium and magnesium concentrations of normal healthy individuals with first time diagnosed patients of valvular heart disease and myocardial infarction as well as to evaluate the prognostic value in the severity and outcome of valvular heart disease and myocardial infarction.Following biochemical tests, the mean serum sodium concentrations in both valvular heart disease and myocardial infarction patients were signifi cantly (p ˂ 0.05) higher than normal healthy persons. The mean potassium and calcium concentrations in valvular heart disease and myocardial patients were signifi cantly (p ˂ 0.05) high and low respectively when compared with normal healthy individuals. In comparison to normal healthy persons, respective groups of valvular heart disease and myocardial infarction patients showed a non-signifi cant (p = 0.6123) and a signifi cant (p ˂ 0.05) reduction in mean serum magnesium concentrations. Moreover, comparative analysis of mean serum electrolytes among valvular heart disease and myocardial infarction patients showed a signifi cant low sodium, high potassium, calcium and magnesium concentrations in contrast to signifi cant high sodium, low potassium, calcium and magnesium concentrations respectively.
JHK Architecten heeft verschillende projecten op het gebied van interieur en herinrichting waarin "Het Nieuwe Werken" en hergebruik centraal staan. In deze presentatie staan enkele voorbeelden hiervan.
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PREVENTION OF HEART PROBLEM USING ARTIFICIAL INTELLIGENCEijaia
Heart is the most important organ of a human body as it not only circulates oxygen and other vital
nutrients through blood to different parts of the body and helping in the metabolic activities but also
removes metabolic wastes. Thus, even a minor problem can affect the whole organism. Hence, researchers
are diverting a lot of data analysis work for assisting the doctors to predict the heart problem. So, an
analysis of the data related to different health problems and its functioning can help in predicting with a
certain probability for the wellness of this organ. In this paper we have analysed the different prescribed
data of patients from different parts of India. Using this data, we have built a model which gets trained
using this data and tries to predict whether a new out-of-sample data has a probability of having any heart
attack or not. This model can help in the decision making along with the doctor to treat the patient well and
creating a transparency between the doctor and the patient. In the validation set of the data, it’s not only
the accuracy that the model has to take care, rather the True Positive Rate and False-Negative Rate along
with the AUC-ROC helps in building/fixing the algorithm inside the model.
Goal attainments and their discrepancies for low density lipoprotein choleste...Paul Schoenhagen
Purpose: Low density lipoprotein cholesterol (LDL-C) is primary treatment target for patients with dislipidemia. The apolipoprotein B (apo B), an emerging biomarker for cardiovascular risk prediction, appears to be superior to the LDL-C. However, little is known about goal attainments and their discrepancies for LDL-C and apo B in Chinese patients with known CAD or DM.
Diagnosis of Early Risks, Management of Risks, and Reduction of Vascular Dise...asclepiuspdfs
In a recent issue of the Journal of Circulation, American Heart Association has published a scientific statement, related to the excess heart disease and acute vascular events in South Asians living in the USA. The same group of experts, also have published a complementary article in Circulation titled, “call to action: Cardiovascular disease (CVD) in Asian Americans.”I being a South Asian immigrant living in the USA, have always wondered as to why we do not have the same benefits as the other resident Americans in terms of the advantages of living in a highly advanced country? According to a study done in 2013, cardiovascular mortality has declined and diabetes mortality has increased in high-income countries. The study done in 26 industrialized nations, estimated the potential role of trends in population, for body mass index, systolic blood pressure, serum total cholesterol, and smoking, the modifiable risk factors identified as the promoters of CVD, and acute vascular events, by the Framingham Heart Study (FHS) group.
Logistic Regression: Predicting The Chances Of Coronary Heart DiseaseMichael Lieberman
Logistic Regression - Predicting the Chances of Coronary Heart Disease weighs risks factors for heart disease and calculates the odds of contracting the disease within the next ten years.
A N NA L S O F FA M I LY M E D I C I N E ✦ W W W. A N N FA.docxransayo
A N NA L S O F FA M I LY M E D I C I N E ✦ W W W. A N N FA M M E D . O R G ✦ VO L . 6 , N O. 6 ✦ N OV E M B E R / D E C E M B E R 2 0 0 8
497
Racial Disparity in Hypertension Control:
Tallying the Death Toll
ABSTRACT
PURPOSE Black Americans with hypertension have poorer blood pressure control
than their white counterparts, but the impact of this disparity on mortality among
black adults is not known. We assessed differences in systolic blood pressure (SBP)
control among white and black adults with a diagnosis of hypertension, and mea-
sured the impact of that difference on cardiovascular and cerebrovascular mortality
among blacks.
METHODS Using SBP measurements from white and black adults participating in
the National Health and Nutrition Examination Survey, 1999-2002, we modeled
changes in mortality rates resulting from a reduction of mean SBP among blacks
to that of whites. Our data source for mortality estimates of blacks with hyper-
tension was a meta-analysis of observational studies of SBP; our data source for
reduction in mortality rates was a meta-analysis of SBP treatment trials.
RESULTS The fi nal sample of participants for whom SBP measurements were
available included 1,545 black adults and 1,335 white adults. The mean SBP
among blacks with hypertension was approximately 6 mm Hg higher than that
for the total adult black population and 7 mm Hg higher than that for whites
with hypertension. Within the hypertensive population, a reduction in mean
SBP among blacks to that of whites would reduce the annual number of deaths
among blacks from heart disease by 5,480 and from stroke by 2,190.
CONCLUSIONS Eliminating racial disparity in blood pressure control among
adults with hypertension would substantially reduce the number of deaths
among blacks from both heart disease and stroke. Primary care clinicians should
be particularly diligent when managing hypertension in black patients.
Ann Fam Med 2008;6:497-502. DOI: 10.1370/afm.873.
INTRODUCTION
C
ardiovascular disease, the leading cause of death in the United
States, occurs at the highest rate among black Americans.1 As a
precursor to cardiovascular disease, hypertension is one of the
most important contributors to racial disparities in mortality rate.2 The
age-adjusted prevalence of hypertension is signifi cantly higher among
blacks (39%) than among whites (29%).3 Uncontrolled hypertension has
an enormous impact on the health of minorities,1,4 accounting for up to
one-quarter of all deaths among black adults, primarily from cardiovascu-
lar and cerebrovascular causes.5
Recent data suggest that among persons under treatment for hyperten-
sion, blacks have poorer blood pressure control.3 Only a few studies have
quantifi ed the effects of racial disparities in health care interventions on
the number of deaths among.6,7 To our knowledge, none have quantifi ed
the impact of disparity in hypertension control on black mortality.
To m.
Dive into the forefront of healthcare analytics with our latest project showcase on heart disease classification. Our students at the Boston Institute of Analytics have delved deep into the complexities of heart disease diagnosis using advanced data science and artificial intelligence techniques. Explore the innovative methodologies, insightful findings, and impactful solutions presented in this collection of projects. From predictive modeling to risk assessment, these projects demonstrate the power of data-driven approaches in revolutionizing healthcare. To learn more about our data science and artificial intelligence programs, visit https://bostoninstituteofanalytics.org/data-science-and-artificial-intelligence/.
Dive into the forefront of healthcare analytics with our latest project showcase on heart disease classification. Our students at the Boston Institute of Analytics have delved deep into the complexities of heart disease diagnosis using advanced data science and artificial intelligence techniques. Explore the innovative methodologies, insightful findings, and impactful solutions presented in this collection of projects. From predictive modeling to risk assessment, these projects demonstrate the power of data-driven approaches in revolutionizing healthcare. To learn more about our data science and artificial intelligence programs, visit https://bostoninstituteofanalytics.org/data-science-and-artificial-intelligence/.
1. Heart Data | 1
1
Christy Lee
Dana Alswyan
Thuan Nguyen
Business Analytics Project: Data on Heart Diseases
EXECUTIVE OVERVIEW
We have 2 datasets, LA Heart, which we did a logistic regression, and Cardiovas, which
we ran correlations and multiple regression analyses with respectively. From the LA Heart data,
we found that systolic blood pressure has a high probability of being related to having heart
disease. The Cardiovas data shows that the dependent variables hemoglobin A1C and blood
glucose each have independent variables that are moderately to highly significant to explaining
the outcome of their dependent variable. Therefore, to explain the results of hemoglobin A1C,
one must refer to levels of blood glucose and cholesterol, and take into account the patient’s age
and waist size. Also, to explain outcomes of blood glucose, one must see hemoglobin A1C levels
as well as age and weight.
LA HEART - LOGISTIC REGRESSION
The data for LA Heart was recorded in 1950. We analyzed three variables: cholesterol,
diastolic blood pressure, systolic blood pressure, and socioeconomic status, against whether the
patients under analysis are ill in terms of complications found in their cardiovascular system. The
dataset has 200 observations; 171 of those observations are healthy patients and 29 people are ill
patients.
We ran a binary logistic regression as a means to generate a probabilistic statistical
classification for the analysed variables. Convergence status per each independent variable has
been satisfied. Our dependent variable was whether the patient was ill (with some sort of heart
condition), and what role the following variables played in them being ill: systolic blood pressure
(mm Hg), diastolic blood pressure (mm Hg), cholesterol (mg%), and socioeconomic status
(Ordinal; 1=high,...,5=low).
The predictive power of the model, which is < 0.0001, is high since the p value is less
than 0.05, as seen in Figure 1. This means the prediction is significant, which is valuable to put
to practical reference.
2. Heart Data | 2
2
Figure 1. LA Heart Predictive Power
Our findings are also concordant; the log odds of the first observation are higher than the
second one. The model was predicted correctly, as seen in Figure 2.
Figure 2. LA Heart Concordance
The ROC curve testing showcases that the area under the curve= 0.9141 which is
classified as excellent (A). This attests to the accuracy of the test we ran as a whole.
Figure 3. LA Heart ROC Curve
3. Heart Data | 3
3
LA HEART - KEY FINDINGS
The 95% confidence interval for SBP_50 lies entirely above 1 to 1 odds, so we are
confident that the odds go up with (SBP_50), the log odds are positive. In Figure 4, we see the
variable with the highest confidence is SBP_50, so we can infer that as SBP_50 goes up, the
odds of having heart problems also increases. The 95% confidence interval of the variables
(DBP_50), (SES), and (CHOL_50) lie on both sides of 1 to 1 odds line, so we aren’t confident
that the odds go either up or down with the three variables mentioned above. The log odds
coefficient is not significant. The confidence interval for SES is especially broad, thus it is the
variable with the least confident odds.
Figure 4. LA Heart Odds Ratios
Also, the influence diagnostics show that the there are some data points that will
influence the confidence levels of each variable versus whether the patient is ill or not. For
example, the influence diagnostic graph for SES shows there are many data points that are far
from 0. Since there is a widespread, the confidence levels for SES are the widest/least confident,
as seen in Figure 5.
4. Heart Data | 4
4
Figure 5. LA Heart Influence Diagnostics
LA HEART - RESULTS
Our results show that the probability of having heart disease being related to the systolic
blood pressure is high. We see this from the influence diagnostics and how the spread for
SBP_50 is tighter compared to the other variables that were compared. Also, we have high
confidence as seen in Figure 4, that SBP_50 is probable due to it having both confidence limits
above 1, and the 95% confidence is also close together, indicating measurable and consistent
results. Socio-economic status has little to do with the probability of having heart disease, while
the other variables have weak probabilities.
CARDIOVAS - CORRELATION
The Cardiovas dataset consists of cardiovascular risk factor data, with 403 observations.
We first conducted a correlation analysis to see which variables would be most useful in our
linear and multiple regressions. We decided cholesterol, systolic blood pressure, and hemoglobin
A1C were dependent variables due to our correlation analysis in Figure 6. We conducted a
multiple regression for each dependent variable, each with 8 independent (explanatory)
variables.
5. Heart Data | 5
5
Figure 6. Cardiovas Correlation Analysis
The slightest blood glucose increase raises the risk of having heart disease.1
An increase
of cholesterol in the blood will build up in the walls of the arteries causing what is known as
“atherosclerosis”. There are two forms of cholesterol: Low-density lipoprotein LDL and it’s
known as “bad” cholesterol, and high-density lipoprotein HDL "good" cholesterol.2
We did not
include HDL as a factor in the analysis due to the fact that it is “good” cholesterol, while there
was no data found for LDL in the data set we selected. For the age factor, it is known that as
people grow older, the heart goes through many physiological changes; age could compound the
problems related to the heart if a cardiovascular disease existed.3
According to WebMD research,
people over the age of 50 have the highest chance of getting heart disease.
CARDIOVAS - LINEAR REGRESSION
In most people, systolic blood pressure rises steadily with age due to increasing stiffness
of large arteries, long-term build-up of plaque, and increased incidence of cardiac and vascular
disease.4
Systolic blood pressure as an independent variable could be a strong predictor for risk
1
MediLexicon International. "Glucose Increases Raise Heart Disease Risk." Medical News Today.
http://www.medicalnewstoday.com/articles/246612.php (accessed December 15, 2013).
2
WebMD. "Cholesterol and Heart Disease." WebMD. http://www.webmd.com/heart-disease/guide/heart-disease-
lower-cholesterol-risk (accessed December 13, 2013).
3
"Heart of the matter." Deccan Herald. http://www.deccanherald.com/content/302951/heart-matter.html (accessed
December 15, 2013).
4
"Understanding Blood Pressure Readings." American Heart Association .
http://www.heart.org/HEARTORG/Conditions/HighBloodPressure/AboutHighBloodPressure/Understanding-Blood-
Pressure-Readings_UCM_301764_Article.jsp# (accessed December 14, 2013).
6. Heart Data | 6
6
of cardiovascular diseases.5
Age also has a strong correlation with systolic blood pressure with a
44.3% correlation; and the r2 value of 19.63% in the linear regression test further proves the
point that systolic blood pressure is explained by age, as seen in Figure 7. Human weight also
plays a big role in showcasing whether a patient is at risk of developing a blockage in the heart.6
But the waist and the hip combined in a ratio are shown to be a better predictor of cardiovascular
diseases than body-mass index.7
Some signs of heart disease include a high level of hemoglobin
A1c. The concentration of hemoglobin A1c in the blood increases the risk for cardiovascular
diseases if found in the blood.8
Figure 7. Cardiovas Linear Regression on Age and Systolic Blood Pressure
In general, the higher the hemoglobin A1C, the higher the risk that a person can will
develop Heart disease. If hemoglobin A1C stays high for a long period of time, the risk for heart
problems is even greater. Our test results show that older people are more likely to have higher
levels of hemoglobin A1C. Diabetesjournals.org reports that hemoglobin A1C levels ≥5.5–6.0%
5
U.S. National Library of Medicine. "Elevated systolic blood pressure and risk of cardiovascular and renal disease."
National Center for Biotechnology Information. http://www.ncbi.nlm.nih.gov/pubmed/10467215 (accessed
December 15, 2013).
6
"Weight & Waistlines: Heart Disease Risk Factors." WebMD. http://www.webmd.com/heart-
disease/features/weight-waistlines-heart-disease-risk (accessed December 15, 2013).
7
Wang, Z. "Waist Circumference, Body Mass Index, Hip Circumference and Waist-To-Hip Ratio as Predictors of
Cardiovascular Disease in Aboriginal People ." UThe University of Queensland.
http://espace.library.uq.edu.au/eserv.php?pid=UQ:9338&dsID=wh.pdf (accessed December 15, 2013).
8
U.S. National Library of Medicine. "Association of hemoglobin A1c with cardiovascular disease and mortality in
adults: the European prospective investigation into cancer in Norfolk.." National Center for Biotechnology
Information. http://www.ncbi.nlm.nih.gov/pubmed/15381514 (accessed December 15, 2013).
7. Heart Data | 7
7
is associated with incident heart failure in a middle-aged population, suggesting that hemoglobin
A1C in relation to older age contributes to development of heart failure.
Figure 8. Cardiovas Correlation of Hemoglobin A1C & Age
Figure 9. Cardiovas Linear Regression of Hemoglobin A1C & Age
CARDIOVAS - MULTIPLE REGRESSION TEST 1: CHOLESTEROL
The independent variables put into SAS against cholesterol are the following: Age, Blood
Glucose, Diastolic Blood Pressure, Hemoglobin A1C, Hip, Systolic Blood Pressure, Waist, and
Weight. We used a stepwise selection and found only 3 independents remained significant:
hemoglobin A1C, age, and diastolic blood pressure.
When looking at the r2
value, or how much each independent variable factors into
affecting cholesterol, diastolic blood pressure shows the highest r2
value with 0.1204. Thus, DBP
8. Heart Data | 8
8
has a 12.04% significance of affecting cholesterol levels. While age and hemoglobin A1C have
r2
values of 0.1002 and 0.0714 respectively
Figure 10. Cardiovas Cholesterol Stepwise Summary
CARDIOVAS - MULTI. REGR. TEST 2: SYSTOLIC BLOOD PRESSURE
The independent variables that are included in the model ran in SAS against systolic
blood pressure are the following: Age, Blood Glucose, Cholesterol, Diastolic Blood Pressure,
Hemoglobin A1C, Hip, Waist, and Weight. The stepwise selection showcased a relation towards
only four independent variables: diastolic blood pressure, age, hip, and weight. The r2
value
results for the variables entered were mostly high indicators with the following numerical values:
0.3686 for diastolic blood pressure which is 36.86% in effect towards systolic blood pressure,
0.5402 for age which is 54.02% as a factor towards the levels of systolic blood pressure, 0.5440
for hip independent variable which is 54.40%, and lastly 0.5476 for the weight factor which
accumulates for 54.76%. All the variables entered showcase a moderate level of significance
towards the dependent variable of systolic blood pressure.
Figure 11. Cardiovas Systolic Blood Pressure Stepwise Summary
CARDIOVAS - MULTI. REGR. TEST 3: HEMOGLOBIN A1C
The independent variables in the the third testing against hemoglobin A1C are as follows:
Age, Blood Glucose, Cholesterol, Diastolic Blood Pressure, Hip, Systolic Blood Pressure, Waist,
and Weight. The stepwise selection showcased a relation towards four independent variables:
blood glucose, cholesterol, age, and waist. The r2
value results for the variables entered
showcases a moderate to high level of significance towards hemoglobin A1C. The numerical
values for the entered variables were the following: 0.5542 for blood glucose which accumulates
for 55.42%, 0.5745 for cholesterol which accumulates for 57.45%, 0.5838 for the age variable
which is 58.38%, and lastly for the waist variable the r2
value showcased a 0.5869 which
accumulates for 58.69%.
9. Heart Data | 9
9
Figure 12. Cardiovas Hemoglobin A1C Stepwise Summary
CARDIOVAS - MULTI. REGR. TEST 4: BLOOD GLUCOSE
The independent variables that are included in the model ran in SAS against Blood
Glucose are the following: Age, Cholesterol, Diastolic Blood Pressure, Hemoglobin A1C, Hip,
Systolic Blood Pressure, Waist, and Weight. The stepwise selection showcased a relation
towards only four independent variables: hemoglobin A1C, weight, and age. The r2
value results
for the variables entered were mostly high indicators with the following numerical values:
0.5542 for hemoglobin A1C which is 55.42% as a factor towards the effect of blood glucose,
0.5579 for the weight variable which accumulates for 55.79%, and lastly 0.5605 for the age
independent variable and that accumulates for 56.05%. All the variables entered showcase a
moderate to high level of significance towards the dependent variable of blood glucose.
Figure 13. Cardiovas Blood Glucose Stepwise Summary
CARDIOVAS - MULTI. REGR. RESULTS
From the previous 4 multiple regressions, hemoglobin A1C’s independent variables as
well as the independent variables for blood glucose have the strongest (moderate-high)
significance to affecting their dependent variable; while the independent variables for systolic
blood pressure have moderate significance towards explaining; and cholesterol’s independent
variables have the weakest (low) significance to explaining the outcome of cholesterol.
Therefore, the independent variables for both hemoglobin A1C and blood glucose should
be referred to in order to explain how the results of each dependent variable came to be.
However, the independent variables for cholesterol, which have a weak significance, should not
be discarded as they still contribute to explaining some part of the outcome of their dependent
variable, albeit a rather small portion of it.
Our most valuable tests are Test 3 and Test 4, as the independent variables in each test
can explain at least 50% of the outcome seen in their dependent variable. Accordingly, to explain
10. Heart Data | 10
10
the results of hemoglobin A1C, levels of blood glucose, cholesterol, the patient’s age and waist
size should be taken into account. Additionally, to explain what affects blood glucose,
hemoglobin A1C levels as well as age and weight must be inspected.
CONCLUSIONS: LA HEART & CARDIOVAS
From the data we found on the LA Heart dataset, our logistic regression test illustrates
systolic blood pressure has a high probability of being related to developing heart disease, while
the other independent variables (diastolic blood pressure, cholesterol, and socioeconomic status)
have less to do with predicting heart illnesses. Both 95% confidence limits of the log odds for
systolic blood pressure are above 1 on the odds line. Influence diagnostics also shows that
systolic blood pressure has the most compact graph, showing that it has strong influence on
having heart illnesses.
The Cardiovas dataset shows us that hemoglobin A1C can be explained the best by waist
size with an r2
value of 0.5869, as seen in Figure 12, which is a moderate to strong significance.
The other independent variables - age, cholesterol, and blood glucose - also have moderate to
high significance to explaining hemoglobin A1C, however, waist size has the highest r2
value of
them all. Additionally, blood glucose can be best explained by the independent variable of age
with an r2
value of 0.5605, as seen in Figure 13. The other independent variables result in
moderate-high significance to affecting blood glucose and they include weight and hemoglobin
A1C.